Semantic Proof of Craig's Interpolation Theorem for Intuitionistic Logic and Extensions, Part II

Abstract

This chapter presents semantic proof of Craig's interpolation theorem for intuitionistic logic and extensions. We shall also refute (in Section 2) the strong form of Robinson's consistency statement for the intuitionistic logic. When in (b) ∅ contains only conjunctions, negations and universal quantifiers. This is the generalization of the translation of the classical propositional logic into the intuitionistic. Craig's interpolation theorem holds for the following extensions of the intuitionistic predicate calculus. The chapter also constructs a theory (Δ(∞), 0), which is for any Δ the classical theory. It is assured that a respective ⊜ ∞ may be found. Thus, two structures S Δ and S θ , which are isomorphic, are obtained.